Question: A school has three clubs and each student is required to belong to exactly one club. One year the students switched club membership as follows:

A school has three clubs and each student is required to belong to exactly one club. One year the students switched club membership as follows:
Club A. 4/10 remain in A, 1/10 switch to B, 5/10 switch to C
Club B. 7/10 remain in B, 2/10 switch to A, 1/10 switch to C
Club C. 6/10 remain in C, 2/10 switch to A, 2/10 switch to C
If the fraction of the student population in each club is unchanged, find each of these fractions.

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